Earth formations may be used for various purposes such as hydrocarbon production, geothermal production, and carbon dioxide sequestration. These reservoirs are typically accessed by drilling boreholes through the earth to the reservoirs.
A borehole is drilled using a drill bit that is rotated by drill pipes coupled together in series and generally referred to as a drill string. A drill rig disposed at the surface of the earth or at the surface of the ocean for ocean drilling applies forces to the drill string and thus to the drill bit for cutting formation rock. The forces may include rotational force or torque for rotating the drill string, weight on the drill bit, and force due to the flow of drilling fluid internal to the drill string. The combination of the drill string forces applied to the drill string result in a rate of penetration into the formation being drilled. It would be appreciated by the drilling industry if a method was developed that estimates a combination of drill string force values or parameters that would improve the rate of penetration and lower the cost of drilling a borehole.